Waning
Note: for some examples, this text may refer to how individuals would move through components of the model. This is an ordinary differential equation (ODE) model, so an “individual” does not have the same definitions as in something like an agent-based model. These example individuals are just for ease of understanding and don’t imply there are individuals in the model in implementation.
In the Scenarios Mechanistic Model waning is defined as a series of bins that populations flow through. Waning is modeled by a two parallel lists of WANING_TIMES and WANING_PROTECTIONS.
WANING_TIMES specifies the average number of timesteps for an individual in some bin wanes into the bin below. Waning bin 0, at index 0 is the most recent bin, meaning infection or vaccination happened most recently. The higher the index, the longer it has been since the average individual recovered from infection or was vaccinated.
WANING_TIMES are also used to initialize the population into waning bins, given the time since last immunological event (either infection or vaccination).
The inverse of each value in WANING_TIMES is the WANING_RATE or the proportion of the population in bin i that wanes to the bin below, this list is passed to the ODEs to determine waning.
WANING_PROTECTIONS multiply the immunity of populations in some waning bin i by WANING_PROTECTIONS[i]. The values within WANING_PROTECTIONS are between 0-1 and account for the loss of protection due to waning, with 1 meaning no protection lost, and 0 meaning all protection has been lost.
the combination of WANING_RATES and WANING_PROTECTIONS define a waning curve, as populations exponentially decay from bin to bin, having their immunity multiplied by the corresponding coefficients.
Notes:
- by definition the last waning "bin" does not have any individuals waning out of it, the only outflow is by infection or vaccination
- The total immunity to an exposure is calculated using the waning status of a population, but also other factors like the immune history, number of vaccinations, and the challenging strain.
- Due to the nature of the exponential decay from bin to bin, a population's average immunity must be measured to see the waning curve, as again, individuals do not exist.
In Scenario's COVID19 mechanistic model, the average population level immunity follows a curve defined in this paper TODO.
The black dots represent the values within WANING_PROTECTIONS and the number of days between each dot the WANING_TIMES
The code to fit the waning curve can be found here TODO TODO